Properties

Label 80.6.n.d.63.2
Level $80$
Weight $6$
Character 80.63
Analytic conductor $12.831$
Analytic rank $0$
Dimension $20$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 80 = 2^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 80.n (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(12.8307055850\)
Analytic rank: \(0\)
Dimension: \(20\)
Relative dimension: \(10\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} + \cdots)\)
Defining polynomial: \(x^{20} + 271 x^{18} + 109637 x^{16} + 25993614 x^{14} + 5522961902 x^{12} + 881545050522 x^{10} + 133816049059481 x^{8} + 14779507781220031 x^{6} + 824105698447750789 x^{4} + 12044868290803250652 x^{2} + 579398322543528055824\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{65}\cdot 3^{4}\cdot 5^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 63.2
Root \(3.75557 - 3.81117i\) of defining polynomial
Character \(\chi\) \(=\) 80.63
Dual form 80.6.n.d.47.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-17.2921 + 17.2921i) q^{3} +(46.1930 - 31.4834i) q^{5} +(154.079 + 154.079i) q^{7} -355.037i q^{9} +O(q^{10})\) \(q+(-17.2921 + 17.2921i) q^{3} +(46.1930 - 31.4834i) q^{5} +(154.079 + 154.079i) q^{7} -355.037i q^{9} -127.489i q^{11} +(335.067 + 335.067i) q^{13} +(-254.362 + 1343.19i) q^{15} +(-1155.01 + 1155.01i) q^{17} +28.2166 q^{19} -5328.70 q^{21} +(-2783.04 + 2783.04i) q^{23} +(1142.60 - 2908.63i) q^{25} +(1937.35 + 1937.35i) q^{27} +3388.31i q^{29} +5384.41i q^{31} +(2204.56 + 2204.56i) q^{33} +(11968.3 + 2266.45i) q^{35} +(11534.0 - 11534.0i) q^{37} -11588.1 q^{39} -11147.8 q^{41} +(-1437.07 + 1437.07i) q^{43} +(-11177.7 - 16400.2i) q^{45} +(-219.040 - 219.040i) q^{47} +30673.4i q^{49} -39945.1i q^{51} +(22745.6 + 22745.6i) q^{53} +(-4013.79 - 5889.12i) q^{55} +(-487.926 + 487.926i) q^{57} -22196.6 q^{59} -1431.25 q^{61} +(54703.5 - 54703.5i) q^{63} +(26026.8 + 4928.73i) q^{65} +(-28948.2 - 28948.2i) q^{67} -96249.3i q^{69} +24188.3i q^{71} +(28574.8 + 28574.8i) q^{73} +(30538.4 + 70054.3i) q^{75} +(19643.4 - 19643.4i) q^{77} +23417.0 q^{79} +19271.9 q^{81} +(-18919.5 + 18919.5i) q^{83} +(-16989.8 + 89716.9i) q^{85} +(-58591.1 - 58591.1i) q^{87} -8179.53i q^{89} +103253. i q^{91} +(-93107.9 - 93107.9i) q^{93} +(1303.41 - 888.354i) q^{95} +(-76747.2 + 76747.2i) q^{97} -45263.4 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20q - 44q^{5} + O(q^{10}) \) \( 20q - 44q^{5} + 804q^{13} - 2236q^{17} - 4520q^{21} + 948q^{25} - 11096q^{33} + 44260q^{37} - 6760q^{41} - 92816q^{45} + 182452q^{53} - 34288q^{57} - 41080q^{61} - 155772q^{65} + 264372q^{73} + 399304q^{77} - 520220q^{81} - 344796q^{85} + 713496q^{93} + 374772q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/80\mathbb{Z}\right)^\times\).

\(n\) \(17\) \(21\) \(31\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(1\) \(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −17.2921 + 17.2921i −1.10929 + 1.10929i −0.116048 + 0.993244i \(0.537023\pi\)
−0.993244 + 0.116048i \(0.962977\pi\)
\(4\) 0 0
\(5\) 46.1930 31.4834i 0.826326 0.563192i
\(6\) 0 0
\(7\) 154.079 + 154.079i 1.18849 + 1.18849i 0.977484 + 0.211011i \(0.0676755\pi\)
0.211011 + 0.977484i \(0.432324\pi\)
\(8\) 0 0
\(9\) 355.037i 1.46106i
\(10\) 0 0
\(11\) 127.489i 0.317682i −0.987304 0.158841i \(-0.949224\pi\)
0.987304 0.158841i \(-0.0507757\pi\)
\(12\) 0 0
\(13\) 335.067 + 335.067i 0.549887 + 0.549887i 0.926408 0.376521i \(-0.122880\pi\)
−0.376521 + 0.926408i \(0.622880\pi\)
\(14\) 0 0
\(15\) −254.362 + 1343.19i −0.291893 + 1.54138i
\(16\) 0 0
\(17\) −1155.01 + 1155.01i −0.969310 + 0.969310i −0.999543 0.0302331i \(-0.990375\pi\)
0.0302331 + 0.999543i \(0.490375\pi\)
\(18\) 0 0
\(19\) 28.2166 0.0179317 0.00896584 0.999960i \(-0.497146\pi\)
0.00896584 + 0.999960i \(0.497146\pi\)
\(20\) 0 0
\(21\) −5328.70 −2.63677
\(22\) 0 0
\(23\) −2783.04 + 2783.04i −1.09698 + 1.09698i −0.102219 + 0.994762i \(0.532594\pi\)
−0.994762 + 0.102219i \(0.967406\pi\)
\(24\) 0 0
\(25\) 1142.60 2908.63i 0.365631 0.930760i
\(26\) 0 0
\(27\) 1937.35 + 1937.35i 0.511446 + 0.511446i
\(28\) 0 0
\(29\) 3388.31i 0.748149i 0.927399 + 0.374074i \(0.122040\pi\)
−0.927399 + 0.374074i \(0.877960\pi\)
\(30\) 0 0
\(31\) 5384.41i 1.00631i 0.864195 + 0.503157i \(0.167828\pi\)
−0.864195 + 0.503157i \(0.832172\pi\)
\(32\) 0 0
\(33\) 2204.56 + 2204.56i 0.352402 + 0.352402i
\(34\) 0 0
\(35\) 11968.3 + 2266.45i 1.65143 + 0.312734i
\(36\) 0 0
\(37\) 11534.0 11534.0i 1.38508 1.38508i 0.549757 0.835324i \(-0.314720\pi\)
0.835324 0.549757i \(-0.185280\pi\)
\(38\) 0 0
\(39\) −11588.1 −1.21997
\(40\) 0 0
\(41\) −11147.8 −1.03569 −0.517844 0.855475i \(-0.673265\pi\)
−0.517844 + 0.855475i \(0.673265\pi\)
\(42\) 0 0
\(43\) −1437.07 + 1437.07i −0.118524 + 0.118524i −0.763881 0.645357i \(-0.776709\pi\)
0.645357 + 0.763881i \(0.276709\pi\)
\(44\) 0 0
\(45\) −11177.7 16400.2i −0.822855 1.20731i
\(46\) 0 0
\(47\) −219.040 219.040i −0.0144637 0.0144637i 0.699838 0.714302i \(-0.253256\pi\)
−0.714302 + 0.699838i \(0.753256\pi\)
\(48\) 0 0
\(49\) 30673.4i 1.82504i
\(50\) 0 0
\(51\) 39945.1i 2.15049i
\(52\) 0 0
\(53\) 22745.6 + 22745.6i 1.11226 + 1.11226i 0.992844 + 0.119421i \(0.0381037\pi\)
0.119421 + 0.992844i \(0.461896\pi\)
\(54\) 0 0
\(55\) −4013.79 5889.12i −0.178916 0.262509i
\(56\) 0 0
\(57\) −487.926 + 487.926i −0.0198915 + 0.0198915i
\(58\) 0 0
\(59\) −22196.6 −0.830149 −0.415074 0.909787i \(-0.636244\pi\)
−0.415074 + 0.909787i \(0.636244\pi\)
\(60\) 0 0
\(61\) −1431.25 −0.0492484 −0.0246242 0.999697i \(-0.507839\pi\)
−0.0246242 + 0.999697i \(0.507839\pi\)
\(62\) 0 0
\(63\) 54703.5 54703.5i 1.73646 1.73646i
\(64\) 0 0
\(65\) 26026.8 + 4928.73i 0.764078 + 0.144694i
\(66\) 0 0
\(67\) −28948.2 28948.2i −0.787835 0.787835i 0.193304 0.981139i \(-0.438080\pi\)
−0.981139 + 0.193304i \(0.938080\pi\)
\(68\) 0 0
\(69\) 96249.3i 2.43374i
\(70\) 0 0
\(71\) 24188.3i 0.569456i 0.958608 + 0.284728i \(0.0919032\pi\)
−0.958608 + 0.284728i \(0.908097\pi\)
\(72\) 0 0
\(73\) 28574.8 + 28574.8i 0.627591 + 0.627591i 0.947461 0.319871i \(-0.103639\pi\)
−0.319871 + 0.947461i \(0.603639\pi\)
\(74\) 0 0
\(75\) 30538.4 + 70054.3i 0.626894 + 1.43808i
\(76\) 0 0
\(77\) 19643.4 19643.4i 0.377563 0.377563i
\(78\) 0 0
\(79\) 23417.0 0.422147 0.211073 0.977470i \(-0.432304\pi\)
0.211073 + 0.977470i \(0.432304\pi\)
\(80\) 0 0
\(81\) 19271.9 0.326371
\(82\) 0 0
\(83\) −18919.5 + 18919.5i −0.301450 + 0.301450i −0.841581 0.540131i \(-0.818375\pi\)
0.540131 + 0.841581i \(0.318375\pi\)
\(84\) 0 0
\(85\) −16989.8 + 89716.9i −0.255059 + 1.34687i
\(86\) 0 0
\(87\) −58591.1 58591.1i −0.829915 0.829915i
\(88\) 0 0
\(89\) 8179.53i 0.109459i −0.998501 0.0547297i \(-0.982570\pi\)
0.998501 0.0547297i \(-0.0174297\pi\)
\(90\) 0 0
\(91\) 103253.i 1.30708i
\(92\) 0 0
\(93\) −93107.9 93107.9i −1.11630 1.11630i
\(94\) 0 0
\(95\) 1303.41 888.354i 0.0148174 0.0100990i
\(96\) 0 0
\(97\) −76747.2 + 76747.2i −0.828196 + 0.828196i −0.987267 0.159071i \(-0.949150\pi\)
0.159071 + 0.987267i \(0.449150\pi\)
\(98\) 0 0
\(99\) −45263.4 −0.464151
\(100\) 0 0
\(101\) −1379.60 −0.0134570 −0.00672851 0.999977i \(-0.502142\pi\)
−0.00672851 + 0.999977i \(0.502142\pi\)
\(102\) 0 0
\(103\) 127370. 127370.i 1.18297 1.18297i 0.203994 0.978972i \(-0.434608\pi\)
0.978972 0.203994i \(-0.0653924\pi\)
\(104\) 0 0
\(105\) −246149. + 167765.i −2.17884 + 1.48501i
\(106\) 0 0
\(107\) −17327.3 17327.3i −0.146309 0.146309i 0.630158 0.776467i \(-0.282990\pi\)
−0.776467 + 0.630158i \(0.782990\pi\)
\(108\) 0 0
\(109\) 105777.i 0.852759i −0.904544 0.426379i \(-0.859789\pi\)
0.904544 0.426379i \(-0.140211\pi\)
\(110\) 0 0
\(111\) 398895.i 3.07292i
\(112\) 0 0
\(113\) 63449.7 + 63449.7i 0.467449 + 0.467449i 0.901087 0.433638i \(-0.142770\pi\)
−0.433638 + 0.901087i \(0.642770\pi\)
\(114\) 0 0
\(115\) −40937.6 + 216176.i −0.288654 + 1.52428i
\(116\) 0 0
\(117\) 118961. 118961.i 0.803416 0.803416i
\(118\) 0 0
\(119\) −355924. −2.30404
\(120\) 0 0
\(121\) 144797. 0.899078
\(122\) 0 0
\(123\) 192769. 192769.i 1.14888 1.14888i
\(124\) 0 0
\(125\) −38793.3 170331.i −0.222066 0.975032i
\(126\) 0 0
\(127\) 150685. + 150685.i 0.829009 + 0.829009i 0.987380 0.158370i \(-0.0506240\pi\)
−0.158370 + 0.987380i \(0.550624\pi\)
\(128\) 0 0
\(129\) 49700.1i 0.262956i
\(130\) 0 0
\(131\) 218406.i 1.11195i −0.831199 0.555976i \(-0.812345\pi\)
0.831199 0.555976i \(-0.187655\pi\)
\(132\) 0 0
\(133\) 4347.58 + 4347.58i 0.0213117 + 0.0213117i
\(134\) 0 0
\(135\) 150487. + 28497.9i 0.710663 + 0.134579i
\(136\) 0 0
\(137\) 48858.6 48858.6i 0.222403 0.222403i −0.587107 0.809509i \(-0.699733\pi\)
0.809509 + 0.587107i \(0.199733\pi\)
\(138\) 0 0
\(139\) 356608. 1.56550 0.782752 0.622334i \(-0.213815\pi\)
0.782752 + 0.622334i \(0.213815\pi\)
\(140\) 0 0
\(141\) 7575.36 0.0320889
\(142\) 0 0
\(143\) 42717.5 42717.5i 0.174689 0.174689i
\(144\) 0 0
\(145\) 106675. + 156516.i 0.421351 + 0.618215i
\(146\) 0 0
\(147\) −530409. 530409.i −2.02450 2.02450i
\(148\) 0 0
\(149\) 39079.0i 0.144204i −0.997397 0.0721022i \(-0.977029\pi\)
0.997397 0.0721022i \(-0.0229708\pi\)
\(150\) 0 0
\(151\) 355671.i 1.26942i −0.772750 0.634711i \(-0.781119\pi\)
0.772750 0.634711i \(-0.218881\pi\)
\(152\) 0 0
\(153\) 410070. + 410070.i 1.41622 + 1.41622i
\(154\) 0 0
\(155\) 169519. + 248722.i 0.566748 + 0.831544i
\(156\) 0 0
\(157\) −37305.0 + 37305.0i −0.120786 + 0.120786i −0.764916 0.644130i \(-0.777220\pi\)
0.644130 + 0.764916i \(0.277220\pi\)
\(158\) 0 0
\(159\) −786641. −2.46765
\(160\) 0 0
\(161\) −857612. −2.60751
\(162\) 0 0
\(163\) 180954. 180954.i 0.533458 0.533458i −0.388142 0.921600i \(-0.626883\pi\)
0.921600 + 0.388142i \(0.126883\pi\)
\(164\) 0 0
\(165\) 171243. + 32428.4i 0.489668 + 0.0927291i
\(166\) 0 0
\(167\) −174882. 174882.i −0.485236 0.485236i 0.421563 0.906799i \(-0.361482\pi\)
−0.906799 + 0.421563i \(0.861482\pi\)
\(168\) 0 0
\(169\) 146753.i 0.395249i
\(170\) 0 0
\(171\) 10017.9i 0.0261992i
\(172\) 0 0
\(173\) 376164. + 376164.i 0.955568 + 0.955568i 0.999054 0.0434856i \(-0.0138463\pi\)
−0.0434856 + 0.999054i \(0.513846\pi\)
\(174\) 0 0
\(175\) 624206. 272107.i 1.54075 0.671653i
\(176\) 0 0
\(177\) 383826. 383826.i 0.920877 0.920877i
\(178\) 0 0
\(179\) 384984. 0.898070 0.449035 0.893514i \(-0.351768\pi\)
0.449035 + 0.893514i \(0.351768\pi\)
\(180\) 0 0
\(181\) −332337. −0.754020 −0.377010 0.926209i \(-0.623048\pi\)
−0.377010 + 0.926209i \(0.623048\pi\)
\(182\) 0 0
\(183\) 24749.5 24749.5i 0.0546308 0.0546308i
\(184\) 0 0
\(185\) 169661. 895919.i 0.364463 1.92460i
\(186\) 0 0
\(187\) 147251. + 147251.i 0.307932 + 0.307932i
\(188\) 0 0
\(189\) 597010.i 1.21570i
\(190\) 0 0
\(191\) 164553.i 0.326378i −0.986595 0.163189i \(-0.947822\pi\)
0.986595 0.163189i \(-0.0521781\pi\)
\(192\) 0 0
\(193\) −58078.0 58078.0i −0.112232 0.112232i 0.648760 0.760993i \(-0.275288\pi\)
−0.760993 + 0.648760i \(0.775288\pi\)
\(194\) 0 0
\(195\) −535288. + 364831.i −1.00809 + 0.687077i
\(196\) 0 0
\(197\) 386719. 386719.i 0.709954 0.709954i −0.256571 0.966525i \(-0.582593\pi\)
0.966525 + 0.256571i \(0.0825929\pi\)
\(198\) 0 0
\(199\) 14055.2 0.0251596 0.0125798 0.999921i \(-0.495996\pi\)
0.0125798 + 0.999921i \(0.495996\pi\)
\(200\) 0 0
\(201\) 1.00115e6 1.74788
\(202\) 0 0
\(203\) −522066. + 522066.i −0.889171 + 0.889171i
\(204\) 0 0
\(205\) −514950. + 350970.i −0.855816 + 0.583291i
\(206\) 0 0
\(207\) 988080. + 988080.i 1.60275 + 1.60275i
\(208\) 0 0
\(209\) 3597.32i 0.00569657i
\(210\) 0 0
\(211\) 438963.i 0.678768i 0.940648 + 0.339384i \(0.110219\pi\)
−0.940648 + 0.339384i \(0.889781\pi\)
\(212\) 0 0
\(213\) −418268. 418268.i −0.631692 0.631692i
\(214\) 0 0
\(215\) −21138.9 + 111627.i −0.0311878 + 0.164691i
\(216\) 0 0
\(217\) −829622. + 829622.i −1.19600 + 1.19600i
\(218\) 0 0
\(219\) −988240. −1.39236
\(220\) 0 0
\(221\) −774010. −1.06602
\(222\) 0 0
\(223\) 413890. 413890.i 0.557343 0.557343i −0.371207 0.928550i \(-0.621056\pi\)
0.928550 + 0.371207i \(0.121056\pi\)
\(224\) 0 0
\(225\) −1.03267e6 405663.i −1.35989 0.534207i
\(226\) 0 0
\(227\) −165742. 165742.i −0.213485 0.213485i 0.592261 0.805746i \(-0.298235\pi\)
−0.805746 + 0.592261i \(0.798235\pi\)
\(228\) 0 0
\(229\) 590717.i 0.744373i 0.928158 + 0.372187i \(0.121392\pi\)
−0.928158 + 0.372187i \(0.878608\pi\)
\(230\) 0 0
\(231\) 679352.i 0.837655i
\(232\) 0 0
\(233\) −849795. 849795.i −1.02547 1.02547i −0.999667 0.0258063i \(-0.991785\pi\)
−0.0258063 0.999667i \(-0.508215\pi\)
\(234\) 0 0
\(235\) −17014.3 3222.02i −0.0200976 0.00380591i
\(236\) 0 0
\(237\) −404930. + 404930.i −0.468284 + 0.468284i
\(238\) 0 0
\(239\) 72025.5 0.0815627 0.0407814 0.999168i \(-0.487015\pi\)
0.0407814 + 0.999168i \(0.487015\pi\)
\(240\) 0 0
\(241\) 358847. 0.397985 0.198992 0.980001i \(-0.436233\pi\)
0.198992 + 0.980001i \(0.436233\pi\)
\(242\) 0 0
\(243\) −804029. + 804029.i −0.873486 + 0.873486i
\(244\) 0 0
\(245\) 965703. + 1.41690e6i 1.02785 + 1.50808i
\(246\) 0 0
\(247\) 9454.46 + 9454.46i 0.00986040 + 0.00986040i
\(248\) 0 0
\(249\) 654318.i 0.668791i
\(250\) 0 0
\(251\) 209249.i 0.209642i −0.994491 0.104821i \(-0.966573\pi\)
0.994491 0.104821i \(-0.0334270\pi\)
\(252\) 0 0
\(253\) 354807. + 354807.i 0.348491 + 0.348491i
\(254\) 0 0
\(255\) −1.25761e6 1.84519e6i −1.21114 1.77701i
\(256\) 0 0
\(257\) −228218. + 228218.i −0.215535 + 0.215535i −0.806614 0.591079i \(-0.798702\pi\)
0.591079 + 0.806614i \(0.298702\pi\)
\(258\) 0 0
\(259\) 3.55428e6 3.29232
\(260\) 0 0
\(261\) 1.20297e6 1.09309
\(262\) 0 0
\(263\) −945242. + 945242.i −0.842663 + 0.842663i −0.989204 0.146542i \(-0.953186\pi\)
0.146542 + 0.989204i \(0.453186\pi\)
\(264\) 0 0
\(265\) 1.76680e6 + 334581.i 1.54551 + 0.292675i
\(266\) 0 0
\(267\) 141442. + 141442.i 0.121422 + 0.121422i
\(268\) 0 0
\(269\) 1.56559e6i 1.31916i −0.751635 0.659579i \(-0.770735\pi\)
0.751635 0.659579i \(-0.229265\pi\)
\(270\) 0 0
\(271\) 990821.i 0.819543i 0.912188 + 0.409772i \(0.134392\pi\)
−0.912188 + 0.409772i \(0.865608\pi\)
\(272\) 0 0
\(273\) −1.78547e6 1.78547e6i −1.44993 1.44993i
\(274\) 0 0
\(275\) −370819. 145669.i −0.295685 0.116154i
\(276\) 0 0
\(277\) −174283. + 174283.i −0.136476 + 0.136476i −0.772044 0.635569i \(-0.780766\pi\)
0.635569 + 0.772044i \(0.280766\pi\)
\(278\) 0 0
\(279\) 1.91166e6 1.47028
\(280\) 0 0
\(281\) 2.17766e6 1.64522 0.822609 0.568607i \(-0.192517\pi\)
0.822609 + 0.568607i \(0.192517\pi\)
\(282\) 0 0
\(283\) 502126. 502126.i 0.372689 0.372689i −0.495767 0.868456i \(-0.665113\pi\)
0.868456 + 0.495767i \(0.165113\pi\)
\(284\) 0 0
\(285\) −7177.24 + 37900.3i −0.00523414 + 0.0276396i
\(286\) 0 0
\(287\) −1.71763e6 1.71763e6i −1.23091 1.23091i
\(288\) 0 0
\(289\) 1.24823e6i 0.879123i
\(290\) 0 0
\(291\) 2.65425e6i 1.83742i
\(292\) 0 0
\(293\) 45772.5 + 45772.5i 0.0311484 + 0.0311484i 0.722509 0.691361i \(-0.242989\pi\)
−0.691361 + 0.722509i \(0.742989\pi\)
\(294\) 0 0
\(295\) −1.02533e6 + 698823.i −0.685974 + 0.467533i
\(296\) 0 0
\(297\) 246992. 246992.i 0.162477 0.162477i
\(298\) 0 0
\(299\) −1.86501e6 −1.20643
\(300\) 0 0
\(301\) −442844. −0.281731
\(302\) 0 0
\(303\) 23856.2 23856.2i 0.0149277 0.0149277i
\(304\) 0 0
\(305\) −66114.0 + 45060.7i −0.0406953 + 0.0277363i
\(306\) 0 0
\(307\) 1.39565e6 + 1.39565e6i 0.845144 + 0.845144i 0.989523 0.144379i \(-0.0461183\pi\)
−0.144379 + 0.989523i \(0.546118\pi\)
\(308\) 0 0
\(309\) 4.40498e6i 2.62451i
\(310\) 0 0
\(311\) 1.84115e6i 1.07942i −0.841852 0.539709i \(-0.818534\pi\)
0.841852 0.539709i \(-0.181466\pi\)
\(312\) 0 0
\(313\) 2.22340e6 + 2.22340e6i 1.28279 + 1.28279i 0.939073 + 0.343718i \(0.111686\pi\)
0.343718 + 0.939073i \(0.388314\pi\)
\(314\) 0 0
\(315\) 804672. 4.24918e6i 0.456922 2.41284i
\(316\) 0 0
\(317\) −1.35501e6 + 1.35501e6i −0.757344 + 0.757344i −0.975838 0.218495i \(-0.929885\pi\)
0.218495 + 0.975838i \(0.429885\pi\)
\(318\) 0 0
\(319\) 431973. 0.237673
\(320\) 0 0
\(321\) 599254. 0.324600
\(322\) 0 0
\(323\) −32590.4 + 32590.4i −0.0173814 + 0.0173814i
\(324\) 0 0
\(325\) 1.35743e6 591738.i 0.712868 0.310757i
\(326\) 0 0
\(327\) 1.82912e6 + 1.82912e6i 0.945958 + 0.945958i
\(328\) 0 0
\(329\) 67498.9i 0.0343801i
\(330\) 0 0
\(331\) 2.40493e6i 1.20652i −0.797546 0.603258i \(-0.793869\pi\)
0.797546 0.603258i \(-0.206131\pi\)
\(332\) 0 0
\(333\) −4.09499e6 4.09499e6i −2.02368 2.02368i
\(334\) 0 0
\(335\) −2.24859e6 425819.i −1.09471 0.207307i
\(336\) 0 0
\(337\) −1.72476e6 + 1.72476e6i −0.827284 + 0.827284i −0.987140 0.159856i \(-0.948897\pi\)
0.159856 + 0.987140i \(0.448897\pi\)
\(338\) 0 0
\(339\) −2.19436e6 −1.03707
\(340\) 0 0
\(341\) 686454. 0.319687
\(342\) 0 0
\(343\) −2.13652e6 + 2.13652e6i −0.980554 + 0.980554i
\(344\) 0 0
\(345\) −3.03025e6 4.44605e6i −1.37066 2.01107i
\(346\) 0 0
\(347\) 2.06948e6 + 2.06948e6i 0.922653 + 0.922653i 0.997216 0.0745635i \(-0.0237563\pi\)
−0.0745635 + 0.997216i \(0.523756\pi\)
\(348\) 0 0
\(349\) 1.88338e6i 0.827702i 0.910345 + 0.413851i \(0.135817\pi\)
−0.910345 + 0.413851i \(0.864183\pi\)
\(350\) 0 0
\(351\) 1.29829e6i 0.562475i
\(352\) 0 0
\(353\) 1.77943e6 + 1.77943e6i 0.760054 + 0.760054i 0.976332 0.216278i \(-0.0693916\pi\)
−0.216278 + 0.976332i \(0.569392\pi\)
\(354\) 0 0
\(355\) 761530. + 1.11733e6i 0.320713 + 0.470556i
\(356\) 0 0
\(357\) 6.15469e6 6.15469e6i 2.55585 2.55585i
\(358\) 0 0
\(359\) 4.50238e6 1.84377 0.921884 0.387466i \(-0.126650\pi\)
0.921884 + 0.387466i \(0.126650\pi\)
\(360\) 0 0
\(361\) −2.47530e6 −0.999678
\(362\) 0 0
\(363\) −2.50386e6 + 2.50386e6i −0.997340 + 0.997340i
\(364\) 0 0
\(365\) 2.21959e6 + 420327.i 0.872049 + 0.165141i
\(366\) 0 0
\(367\) −604369. 604369.i −0.234227 0.234227i 0.580227 0.814455i \(-0.302964\pi\)
−0.814455 + 0.580227i \(0.802964\pi\)
\(368\) 0 0
\(369\) 3.95787e6i 1.51320i
\(370\) 0 0
\(371\) 7.00922e6i 2.64384i
\(372\) 0 0
\(373\) 87601.5 + 87601.5i 0.0326016 + 0.0326016i 0.723220 0.690618i \(-0.242661\pi\)
−0.690618 + 0.723220i \(0.742661\pi\)
\(374\) 0 0
\(375\) 3.61621e6 + 2.27457e6i 1.32793 + 0.835258i
\(376\) 0 0
\(377\) −1.13531e6 + 1.13531e6i −0.411397 + 0.411397i
\(378\) 0 0
\(379\) −2.48550e6 −0.888824 −0.444412 0.895823i \(-0.646587\pi\)
−0.444412 + 0.895823i \(0.646587\pi\)
\(380\) 0 0
\(381\) −5.21132e6 −1.83923
\(382\) 0 0
\(383\) −601337. + 601337.i −0.209470 + 0.209470i −0.804042 0.594572i \(-0.797321\pi\)
0.594572 + 0.804042i \(0.297321\pi\)
\(384\) 0 0
\(385\) 288948. 1.52583e6i 0.0993499 0.524630i
\(386\) 0 0
\(387\) 510213. + 510213.i 0.173171 + 0.173171i
\(388\) 0 0
\(389\) 3.73874e6i 1.25271i −0.779537 0.626356i \(-0.784546\pi\)
0.779537 0.626356i \(-0.215454\pi\)
\(390\) 0 0
\(391\) 6.42886e6i 2.12663i
\(392\) 0 0
\(393\) 3.77670e6 + 3.77670e6i 1.23348 + 1.23348i
\(394\) 0 0
\(395\) 1.08170e6 737246.i 0.348831 0.237750i
\(396\) 0 0
\(397\) −209001. + 209001.i −0.0665538 + 0.0665538i −0.739600 0.673046i \(-0.764985\pi\)
0.673046 + 0.739600i \(0.264985\pi\)
\(398\) 0 0
\(399\) −150358. −0.0472818
\(400\) 0 0
\(401\) −3.88404e6 −1.20621 −0.603104 0.797662i \(-0.706070\pi\)
−0.603104 + 0.797662i \(0.706070\pi\)
\(402\) 0 0
\(403\) −1.80414e6 + 1.80414e6i −0.553359 + 0.553359i
\(404\) 0 0
\(405\) 890227. 606743.i 0.269689 0.183809i
\(406\) 0 0
\(407\) −1.47046e6 1.47046e6i −0.440015 0.440015i
\(408\) 0 0
\(409\) 1.17358e6i 0.346899i −0.984843 0.173450i \(-0.944509\pi\)
0.984843 0.173450i \(-0.0554913\pi\)
\(410\) 0 0
\(411\) 1.68974e6i 0.493419i
\(412\) 0 0
\(413\) −3.42002e6 3.42002e6i −0.986627 0.986627i
\(414\) 0 0
\(415\) −278300. + 1.46960e6i −0.0793219 + 0.418870i
\(416\) 0 0
\(417\) −6.16652e6 + 6.16652e6i −1.73660 + 1.73660i
\(418\) 0 0
\(419\) 1.60340e6 0.446177 0.223089 0.974798i \(-0.428386\pi\)
0.223089 + 0.974798i \(0.428386\pi\)
\(420\) 0 0
\(421\) −3.71020e6 −1.02022 −0.510108 0.860111i \(-0.670394\pi\)
−0.510108 + 0.860111i \(0.670394\pi\)
\(422\) 0 0
\(423\) −77767.4 + 77767.4i −0.0211323 + 0.0211323i
\(424\) 0 0
\(425\) 2.03978e6 + 4.67919e6i 0.547786 + 1.25660i
\(426\) 0 0
\(427\) −220526. 220526.i −0.0585315 0.0585315i
\(428\) 0 0
\(429\) 1.47735e6i 0.387562i
\(430\) 0 0
\(431\) 2.29101e6i 0.594065i −0.954867 0.297033i \(-0.904003\pi\)
0.954867 0.297033i \(-0.0959971\pi\)
\(432\) 0 0
\(433\) −972567. 972567.i −0.249287 0.249287i 0.571391 0.820678i \(-0.306404\pi\)
−0.820678 + 0.571391i \(0.806404\pi\)
\(434\) 0 0
\(435\) −4.55115e6 861857.i −1.15318 0.218380i
\(436\) 0 0
\(437\) −78527.9 + 78527.9i −0.0196707 + 0.0196707i
\(438\) 0 0
\(439\) −3.49284e6 −0.865002 −0.432501 0.901633i \(-0.642369\pi\)
−0.432501 + 0.901633i \(0.642369\pi\)
\(440\) 0 0
\(441\) 1.08902e7 2.66648
\(442\) 0 0
\(443\) 4.91464e6 4.91464e6i 1.18982 1.18982i 0.212707 0.977116i \(-0.431772\pi\)
0.977116 0.212707i \(-0.0682281\pi\)
\(444\) 0 0
\(445\) −257519. 377837.i −0.0616466 0.0904492i
\(446\) 0 0
\(447\) 675761. + 675761.i 0.159965 + 0.159965i
\(448\) 0 0
\(449\) 3.79845e6i 0.889182i −0.895734 0.444591i \(-0.853349\pi\)
0.895734 0.444591i \(-0.146651\pi\)
\(450\) 0 0
\(451\) 1.42122e6i 0.329019i
\(452\) 0 0
\(453\) 6.15031e6 + 6.15031e6i 1.40816 + 1.40816i
\(454\) 0 0
\(455\) 3.25076e6 + 4.76959e6i 0.736134 + 1.08007i
\(456\) 0 0
\(457\) 4.14446e6 4.14446e6i 0.928276 0.928276i −0.0693189 0.997595i \(-0.522083\pi\)
0.997595 + 0.0693189i \(0.0220826\pi\)
\(458\) 0 0
\(459\) −4.47532e6 −0.991499
\(460\) 0 0
\(461\) 1.33612e6 0.292815 0.146407 0.989224i \(-0.453229\pi\)
0.146407 + 0.989224i \(0.453229\pi\)
\(462\) 0 0
\(463\) 3.66263e6 3.66263e6i 0.794036 0.794036i −0.188112 0.982148i \(-0.560237\pi\)
0.982148 + 0.188112i \(0.0602367\pi\)
\(464\) 0 0
\(465\) −7.23229e6 1.36959e6i −1.55111 0.293736i
\(466\) 0 0
\(467\) −4.58287e6 4.58287e6i −0.972401 0.972401i 0.0272279 0.999629i \(-0.491332\pi\)
−0.999629 + 0.0272279i \(0.991332\pi\)
\(468\) 0 0
\(469\) 8.92061e6i 1.87267i
\(470\) 0 0
\(471\) 1.29017e6i 0.267975i
\(472\) 0 0
\(473\) 183211. + 183211.i 0.0376530 + 0.0376530i
\(474\) 0 0
\(475\) 32240.2 82071.6i 0.00655637 0.0166901i
\(476\) 0 0
\(477\) 8.07553e6 8.07553e6i 1.62508 1.62508i
\(478\) 0 0
\(479\) 7.00075e6 1.39414 0.697069 0.717004i \(-0.254487\pi\)
0.697069 + 0.717004i \(0.254487\pi\)
\(480\) 0 0
\(481\) 7.72932e6 1.52328
\(482\) 0 0
\(483\) 1.48300e7 1.48300e7i 2.89249 2.89249i
\(484\) 0 0
\(485\) −1.12893e6 + 5.96145e6i −0.217927 + 1.15079i
\(486\) 0 0
\(487\) −3.98892e6 3.98892e6i −0.762137 0.762137i 0.214571 0.976708i \(-0.431165\pi\)
−0.976708 + 0.214571i \(0.931165\pi\)
\(488\) 0 0
\(489\) 6.25818e6i 1.18352i
\(490\) 0 0
\(491\) 2.30379e6i 0.431260i 0.976475 + 0.215630i \(0.0691805\pi\)
−0.976475 + 0.215630i \(0.930819\pi\)
\(492\) 0 0
\(493\) −3.91352e6 3.91352e6i −0.725188 0.725188i
\(494\) 0 0
\(495\) −2.09085e6 + 1.42504e6i −0.383540 + 0.261406i
\(496\) 0 0
\(497\) −3.72690e6 + 3.72690e6i −0.676795 + 0.676795i
\(498\) 0 0
\(499\) −2.47982e6 −0.445829 −0.222914 0.974838i \(-0.571557\pi\)
−0.222914 + 0.974838i \(0.571557\pi\)
\(500\) 0 0
\(501\) 6.04816e6 1.07654
\(502\) 0 0
\(503\) −4.08077e6 + 4.08077e6i −0.719154 + 0.719154i −0.968432 0.249278i \(-0.919807\pi\)
0.249278 + 0.968432i \(0.419807\pi\)
\(504\) 0 0
\(505\) −63727.8 + 43434.3i −0.0111199 + 0.00757887i
\(506\) 0 0
\(507\) 2.53768e6 + 2.53768e6i 0.438446 + 0.438446i
\(508\) 0 0
\(509\) 2.80205e6i 0.479382i 0.970849 + 0.239691i \(0.0770461\pi\)
−0.970849 + 0.239691i \(0.922954\pi\)
\(510\) 0 0
\(511\) 8.80554e6i 1.49178i
\(512\) 0 0
\(513\) 54665.6 + 54665.6i 0.00917109 + 0.00917109i
\(514\) 0 0
\(515\) 1.87357e6 9.89361e6i 0.311280 1.64375i
\(516\) 0 0
\(517\) −27925.3 + 27925.3i −0.00459485 + 0.00459485i
\(518\) 0 0
\(519\) −1.30094e7 −2.12001
\(520\) 0 0
\(521\) 144765. 0.0233652 0.0116826 0.999932i \(-0.496281\pi\)
0.0116826 + 0.999932i \(0.496281\pi\)
\(522\) 0 0
\(523\) −3.79906e6 + 3.79906e6i −0.607327 + 0.607327i −0.942247 0.334920i \(-0.891291\pi\)
0.334920 + 0.942247i \(0.391291\pi\)
\(524\) 0 0
\(525\) −6.08855e6 + 1.54992e7i −0.964085 + 2.45420i
\(526\) 0 0
\(527\) −6.21903e6 6.21903e6i −0.975430 0.975430i
\(528\) 0 0
\(529\) 9.05423e6i 1.40674i
\(530\) 0 0
\(531\) 7.88060e6i 1.21289i
\(532\) 0 0
\(533\) −3.73526e6 3.73526e6i −0.569511 0.569511i
\(534\) 0 0
\(535\) −1.34593e6 254880.i −0.203300 0.0384991i
\(536\) 0 0
\(537\) −6.65720e6 + 6.65720e6i −0.996221 + 0.996221i
\(538\) 0 0
\(539\) 3.91053e6 0.579781
\(540\) 0 0
\(541\) −1.17321e7 −1.72339 −0.861695 0.507426i \(-0.830597\pi\)
−0.861695 + 0.507426i \(0.830597\pi\)
\(542\) 0 0
\(543\) 5.74683e6 5.74683e6i 0.836428 0.836428i
\(544\) 0 0
\(545\) −3.33023e6 4.88618e6i −0.480267 0.704657i
\(546\) 0 0
\(547\) −5.24186e6 5.24186e6i −0.749060 0.749060i 0.225243 0.974303i \(-0.427683\pi\)
−0.974303 + 0.225243i \(0.927683\pi\)
\(548\) 0 0
\(549\) 508148.i 0.0719547i
\(550\) 0 0
\(551\) 95606.6i 0.0134156i
\(552\) 0 0
\(553\) 3.60806e6 + 3.60806e6i 0.501719 + 0.501719i
\(554\) 0 0
\(555\) 1.25586e7 + 1.84262e7i 1.73064 + 2.53923i
\(556\) 0 0
\(557\) 7.61782e6 7.61782e6i 1.04038 1.04038i 0.0412325 0.999150i \(-0.486872\pi\)
0.999150 0.0412325i \(-0.0131284\pi\)
\(558\) 0 0
\(559\) −963030. −0.130350
\(560\) 0 0
\(561\) −5.09258e6 −0.683173
\(562\) 0 0
\(563\) −86277.5 + 86277.5i −0.0114717 + 0.0114717i −0.712819 0.701348i \(-0.752582\pi\)
0.701348 + 0.712819i \(0.252582\pi\)
\(564\) 0 0
\(565\) 4.92855e6 + 933326.i 0.649528 + 0.123002i
\(566\) 0 0
\(567\) 2.96938e6 + 2.96938e6i 0.387890 + 0.387890i
\(568\) 0 0
\(569\) 5.02097e6i 0.650140i −0.945690 0.325070i \(-0.894612\pi\)
0.945690 0.325070i \(-0.105388\pi\)
\(570\) 0 0
\(571\) 8.08321e6i 1.03751i −0.854922 0.518756i \(-0.826395\pi\)
0.854922 0.518756i \(-0.173605\pi\)
\(572\) 0 0
\(573\) 2.84547e6 + 2.84547e6i 0.362049 + 0.362049i
\(574\) 0 0
\(575\) 4.91492e6 + 1.12747e7i 0.619936 + 1.42212i
\(576\) 0 0
\(577\) −3.25025e6 + 3.25025e6i −0.406422 + 0.406422i −0.880489 0.474067i \(-0.842786\pi\)
0.474067 + 0.880489i \(0.342786\pi\)
\(578\) 0 0
\(579\) 2.00859e6 0.248997
\(580\) 0 0
\(581\) −5.83018e6 −0.716542
\(582\) 0 0
\(583\) 2.89982e6 2.89982e6i 0.353346 0.353346i
\(584\) 0 0
\(585\) 1.74988e6 9.24047e6i 0.211407 1.11636i
\(586\) 0 0
\(587\) 3.79350e6 + 3.79350e6i 0.454407 + 0.454407i 0.896814 0.442407i \(-0.145875\pi\)
−0.442407 + 0.896814i \(0.645875\pi\)
\(588\) 0 0
\(589\) 151930.i 0.0180449i
\(590\) 0 0
\(591\) 1.33744e7i 1.57509i
\(592\) 0 0
\(593\) 1.01322e7 + 1.01322e7i 1.18323 + 1.18323i 0.978904 + 0.204321i \(0.0654987\pi\)
0.204321 + 0.978904i \(0.434501\pi\)
\(594\) 0 0
\(595\) −1.64412e7 + 1.12057e7i −1.90389 + 1.29762i
\(596\) 0 0
\(597\) −243044. + 243044.i −0.0279093 + 0.0279093i
\(598\) 0 0
\(599\) −1.84016e6 −0.209550 −0.104775 0.994496i \(-0.533412\pi\)
−0.104775 + 0.994496i \(0.533412\pi\)
\(600\) 0 0
\(601\) 2.07660e6 0.234513 0.117257 0.993102i \(-0.462590\pi\)
0.117257 + 0.993102i \(0.462590\pi\)
\(602\) 0 0
\(603\) −1.02777e7 + 1.02777e7i −1.15107 + 1.15107i
\(604\) 0 0
\(605\) 6.68864e6 4.55871e6i 0.742932 0.506353i
\(606\) 0 0
\(607\) 7.47671e6 + 7.47671e6i 0.823643 + 0.823643i 0.986628 0.162986i \(-0.0521125\pi\)
−0.162986 + 0.986628i \(0.552112\pi\)
\(608\) 0 0
\(609\) 1.80553e7i 1.97270i
\(610\) 0 0
\(611\) 146786.i 0.0159068i
\(612\) 0 0
\(613\) 421185. + 421185.i 0.0452712 + 0.0452712i 0.729380 0.684109i \(-0.239809\pi\)
−0.684109 + 0.729380i \(0.739809\pi\)
\(614\) 0 0
\(615\) 2.83557e6 1.49736e7i 0.302310 1.59639i
\(616\) 0 0
\(617\) 4.79146e6 4.79146e6i 0.506705 0.506705i −0.406808 0.913514i \(-0.633358\pi\)
0.913514 + 0.406808i \(0.133358\pi\)
\(618\) 0 0
\(619\) −8.81805e6 −0.925009 −0.462505 0.886617i \(-0.653049\pi\)
−0.462505 + 0.886617i \(0.653049\pi\)
\(620\) 0 0
\(621\) −1.07835e7 −1.12209
\(622\) 0 0
\(623\) 1.26029e6 1.26029e6i 0.130092 0.130092i
\(624\) 0 0
\(625\) −7.15458e6 6.64676e6i −0.732629 0.680629i
\(626\) 0 0
\(627\) 62205.4 + 62205.4i 0.00631915 + 0.00631915i
\(628\) 0 0
\(629\) 2.66437e7i 2.68515i
\(630\) 0 0
\(631\) 4.57807e6i 0.457730i −0.973458 0.228865i \(-0.926499\pi\)
0.973458 0.228865i \(-0.0735014\pi\)
\(632\) 0 0
\(633\) −7.59061e6 7.59061e6i −0.752952 0.752952i
\(634\) 0 0
\(635\) 1.17046e7 + 2.21652e6i 1.15192 + 0.218141i
\(636\) 0 0
\(637\) −1.02777e7 + 1.02777e7i −1.00356 + 1.00356i
\(638\) 0 0
\(639\) 8.58774e6 0.832007
\(640\) 0 0
\(641\) −1.62758e7 −1.56458 −0.782288 0.622917i \(-0.785947\pi\)
−0.782288 + 0.622917i \(0.785947\pi\)
\(642\) 0 0
\(643\) −2.99416e6 + 2.99416e6i −0.285593 + 0.285593i −0.835335 0.549742i \(-0.814726\pi\)
0.549742 + 0.835335i \(0.314726\pi\)
\(644\) 0 0
\(645\) −1.56473e6 2.29580e6i −0.148094 0.217287i
\(646\) 0 0
\(647\) 4.92387e6 + 4.92387e6i 0.462430 + 0.462430i 0.899451 0.437021i \(-0.143967\pi\)
−0.437021 + 0.899451i \(0.643967\pi\)
\(648\) 0 0
\(649\) 2.82983e6i 0.263723i
\(650\) 0 0
\(651\) 2.86919e7i 2.65342i
\(652\) 0 0
\(653\) 1.05307e7 + 1.05307e7i 0.966441 + 0.966441i 0.999455 0.0330138i \(-0.0105105\pi\)
−0.0330138 + 0.999455i \(0.510511\pi\)
\(654\) 0 0
\(655\) −6.87615e6 1.00888e7i −0.626241 0.918835i
\(656\) 0 0
\(657\) 1.01451e7 1.01451e7i 0.916945 0.916945i
\(658\) 0 0
\(659\) −1.29023e7 −1.15732 −0.578659 0.815570i \(-0.696424\pi\)
−0.578659 + 0.815570i \(0.696424\pi\)
\(660\) 0 0
\(661\) 6.60437e6 0.587933 0.293967 0.955816i \(-0.405025\pi\)
0.293967 + 0.955816i \(0.405025\pi\)
\(662\) 0 0
\(663\) 1.33843e7 1.33843e7i 1.18253 1.18253i
\(664\) 0 0
\(665\) 337704. + 63951.5i 0.0296130 + 0.00560785i
\(666\) 0 0
\(667\) −9.42978e6 9.42978e6i −0.820705 0.820705i
\(668\) 0 0
\(669\) 1.43141e7i 1.23651i
\(670\) 0 0
\(671\) 182470.i 0.0156453i
\(672\) 0 0
\(673\) 1.01077e7 + 1.01077e7i 0.860230 + 0.860230i 0.991365 0.131135i \(-0.0418621\pi\)
−0.131135 + 0.991365i \(0.541862\pi\)
\(674\) 0 0
\(675\) 7.84865e6 3.42143e6i 0.663034 0.289033i
\(676\) 0 0
\(677\) 5.24850e6 5.24850e6i 0.440112 0.440112i −0.451938 0.892050i \(-0.649267\pi\)
0.892050 + 0.451938i \(0.149267\pi\)
\(678\) 0 0
\(679\) −2.36502e7 −1.96861
\(680\) 0 0
\(681\) 5.73207e6 0.473635
\(682\) 0 0
\(683\) −1.03798e7 + 1.03798e7i −0.851407 + 0.851407i −0.990306 0.138900i \(-0.955643\pi\)
0.138900 + 0.990306i \(0.455643\pi\)
\(684\) 0 0
\(685\) 718695. 3.79516e6i 0.0585218 0.309032i
\(686\) 0 0
\(687\) −1.02148e7 1.02148e7i −0.825727 0.825727i
\(688\) 0 0
\(689\) 1.52426e7i 1.22324i
\(690\) 0 0
\(691\) 6.06155e6i 0.482935i 0.970409 + 0.241468i \(0.0776288\pi\)
−0.970409 + 0.241468i \(0.922371\pi\)
\(692\) 0 0
\(693\) −6.97412e6 6.97412e6i −0.551641 0.551641i
\(694\) 0 0
\(695\) 1.64728e7 1.12272e7i 1.29362 0.881679i
\(696\) 0 0
\(697\) 1.28758e7 1.28758e7i 1.00390 1.00390i
\(698\) 0 0
\(699\) 2.93896e7 2.27510
\(700\) 0 0
\(701\) 2.87503e6 0.220977 0.110489 0.993877i \(-0.464758\pi\)
0.110489 + 0.993877i \(0.464758\pi\)
\(702\) 0 0
\(703\) 325450. 325450.i 0.0248368 0.0248368i
\(704\) 0 0
\(705\) 349929. 238498.i 0.0265159 0.0180722i
\(706\) 0 0
\(707\) −212566. 212566.i −0.0159936 0.0159936i
\(708\) 0 0
\(709\) 528547.i 0.0394883i 0.999805 + 0.0197441i \(0.00628516\pi\)
−0.999805 + 0.0197441i \(0.993715\pi\)
\(710\) 0 0
\(711\) 8.31390e6i 0.616780i
\(712\) 0 0
\(713\) −1.49850e7 1.49850e7i −1.10391 1.10391i
\(714\) 0 0
\(715\) 628360. 3.31814e6i 0.0459667 0.242733i
\(716\) 0 0
\(717\) −1.24548e6 + 1.24548e6i −0.0904769 + 0.0904769i
\(718\) 0 0
\(719\) 1.66055e7 1.19793 0.598963 0.800777i \(-0.295580\pi\)
0.598963 + 0.800777i \(0.295580\pi\)
\(720\) 0 0
\(721\) 3.92498e7 2.81190
\(722\) 0 0
\(723\) −6.20523e6 + 6.20523e6i −0.441481 + 0.441481i
\(724\) 0 0
\(725\) 9.85532e6 + 3.87147e6i 0.696347 + 0.273546i
\(726\) 0 0
\(727\) 1.54075e7 + 1.54075e7i 1.08118 + 1.08118i 0.996400 + 0.0847783i \(0.0270182\pi\)
0.0847783 + 0.996400i \(0.472982\pi\)
\(728\) 0 0
\(729\) 2.31237e7i 1.61153i
\(730\) 0 0
\(731\) 3.31966e6i 0.229773i
\(732\) 0 0
\(733\) −1.69113e7 1.69113e7i −1.16256 1.16256i −0.983913 0.178650i \(-0.942827\pi\)
−0.178650 0.983913i \(-0.557173\pi\)
\(734\) 0 0
\(735\) −4.12003e7 7.80215e6i −2.81308 0.532716i
\(736\) 0 0
\(737\) −3.69059e6 + 3.69059e6i −0.250281 + 0.250281i
\(738\) 0 0
\(739\) 2.76180e7 1.86029 0.930147 0.367187i \(-0.119679\pi\)
0.930147 + 0.367187i \(0.119679\pi\)
\(740\) 0 0
\(741\) −326976. −0.0218761
\(742\) 0 0
\(743\) −1.71922e7 + 1.71922e7i −1.14251 + 1.14251i −0.154521 + 0.987990i \(0.549383\pi\)
−0.987990 + 0.154521i \(0.950617\pi\)
\(744\) 0 0
\(745\) −1.23034e6 1.80518e6i −0.0812147 0.119160i
\(746\) 0 0
\(747\) 6.71712e6 + 6.71712e6i 0.440435 + 0.440435i
\(748\) 0 0
\(749\) 5.33954e6i 0.347776i
\(750\) 0 0
\(751\) 1.11896e7i 0.723961i 0.932186 + 0.361981i \(0.117899\pi\)
−0.932186 + 0.361981i \(0.882101\pi\)
\(752\) 0 0
\(753\) 3.61836e6 + 3.61836e6i 0.232554 + 0.232554i
\(754\) 0 0
\(755\) −1.11977e7 1.64295e7i −0.714928 1.04896i
\(756\) 0 0
\(757\) −1.17247e6 + 1.17247e6i −0.0743637 + 0.0743637i −0.743310 0.668947i \(-0.766745\pi\)
0.668947 + 0.743310i \(0.266745\pi\)
\(758\) 0 0
\(759\) −1.22708e7 −0.773156
\(760\) 0 0
\(761\) −9.79138e6 −0.612890 −0.306445 0.951888i \(-0.599140\pi\)
−0.306445 + 0.951888i \(0.599140\pi\)
\(762\) 0 0
\(763\) 1.62980e7 1.62980e7i 1.01350 1.01350i
\(764\) 0 0
\(765\) 3.18528e7 + 6.03200e6i 1.96786 + 0.372656i
\(766\) 0 0
\(767\) −7.43734e6 7.43734e6i −0.456488 0.456488i
\(768\) 0 0
\(769\) 1.10059e7i 0.671138i 0.942016 + 0.335569i \(0.108929\pi\)
−0.942016 + 0.335569i \(0.891071\pi\)
\(770\) 0 0
\(771\) 7.89277e6i 0.478182i
\(772\) 0 0
\(773\) 8.90959e6 + 8.90959e6i 0.536302 + 0.536302i 0.922441 0.386139i \(-0.126191\pi\)
−0.386139 + 0.922441i \(0.626191\pi\)
\(774\) 0 0
\(775\) 1.56612e7 + 6.15220e6i 0.936637 + 0.367939i
\(776\) 0 0
\(777\) −6.14612e7 + 6.14612e7i −3.65215 + 3.65215i
\(778\) 0 0
\(779\) −314553. −0.0185716
\(780\) 0 0
\(781\) 3.08375e6 0.180906
\(782\) 0 0
\(783\) −6.56435e6 + 6.56435e6i −0.382638 + 0.382638i
\(784\) 0 0
\(785\) −548745. + 2.89772e6i −0.0317831 + 0.167835i
\(786\) 0 0
\(787\) 4.88094e6 + 4.88094e6i 0.280910 + 0.280910i 0.833472 0.552562i \(-0.186350\pi\)
−0.552562 + 0.833472i \(0.686350\pi\)
\(788\) 0 0
\(789\) 3.26905e7i 1.86952i
\(790\) 0 0